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Unformatted text preview: as these assets have a
low correlation with the other assets included in the portfolio.
For a 2 asset portfolio, this equation also suggest: 22
22 P wA A wB B 2wA wB A B Both approaches lead to the same value of portfolio risk. For portfolios with more than 2 assets, it is easier to
use an n-by-n square matrix, commonly known as the variance covariance matrix, to identify all the variance
and covariance terms required to compute . Refer to HY textbook page 71.
As portfolios of unlimited assets of different weightings can be analyzed, we must define some ranking rules to
filter out the inferior portfolios.
2 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 P ORTFOLIO SELECTIONS – I DENTIFYING THE SET OF EFFICIENT PORTFOLIOS
Suppose we have identified a number of risky assets to invest. We then form a number of hypothetical
portfolios, compute their risks and expected returns, and finally p different degrees of risk aversion do not select the same ORP, and
The more risk averse prefers a less risky ORP than the less risk averse. 4 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 L ECTURE 5 – O PTIMAL PORTFOLIOS
B ACKGROUND
Risk free assets are zero risk instruments, in which their rates of return are the risk free rate (rf). For simplicity,
it is generally assumed that investors can borrow and lend at the same risk-free rate & flat and constant term
structure of interest rates. This assumption is later relaxed. T HE CAPITAL ALLOCATION LINE (CAL)
B ALANCED PORTFOLIOS
Risky portfolio – made up of risky assets only.
Balanced portfolio –made up of risk free asset and risky assets. It can be thought of as a 2 asset portfolio –
where 1 is a risky asset, and 1 is a risk free asset.
yp is the proportion of initial wealth allocated to the portfolio of risky assets P. Depending on whether the
investor borrows or lends at the risk free rate, yp may take on any non-negative value. yp = 0 all funds invested in rf
yp > 0 a proportion is invested in rf and P (assuming yp < 1)
yp = 1 if investor doesn’t borrow or lend, and invests all in P
yp > 1 investor borrows and invests in P E( ) ( ) (1 − ) The SD of a balanced portfolio only relates to the wei...
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